Hello. Thanks for taking the time to answer questions.

I have a basement bathroom shower stall that backs up when you flush the toilet.
Also, when you flush the toilet, sometimes it will gurgle and slowly go down but
Then some backs up into the bathroom stall drain.
It has also started to come out under the toilet itself.

What do you think may be the problem and solution?

You have a partial blockage downstream of the basement shower. This back pressure is what makes your toilet gurgle also. The solution would be to snake the drain line. This can be done from several places. You may pull the toiletand snake through the open closet bend, or, you can snake from the basement lavatory roof vent, or, if you have a basement clean out and it's full of water after a flush you may snake from there. Good luck, Tom

That is what I was going to suggest as well.